Face behind transparent material not visible
You aren't doing anything wrong, this is an inherent problem with Unity.  You are looking for a "per-surface" shader, but you are finding out that Unity out-of-the-box is "per-object" (i.e. doesn't show itself through transparency).

The answer to this question does an adequate job of summarizing your problem, and potential solutions:

http://answers.unity3d.com/questions/609021/how-to-fix-transparent-rendering-problem.html

There is nothing you can do on Blender's side.

As for the hole at the bottom:  try a "solidfy" modifier on the bottom.  This will make the base have thickness and will give both sides of the base drawable normals for Unity to pick up on.  Fail that, play with how the normals are calculated (Ctrl+n)